Provision is mad to use data-based function models in order to implement function models in control devices, in particular engine control devices for internal combustion engines. Parameter-free data-based function models are often used, since they can be prepared, without specific stipulations, from training data, i.e. from a set of training data points.
One example of a data-based function model is represented by the so-called Gaussian process model, which is based on Gaussian process regression. Gaussian process regression is a versatile method for data-based modeling of complex physical systems. Regression analysis is based on usually large sets of training data, so that it is useful to utilize approximative solution approaches that can be evaluated more efficiently.
For the Gaussian process model, there exists the possibility of using a sparse Gaussian process regression in which only a representative set of interpolation point data is used to prepare the data-based function model. The interpolation point data must be appropriately selected from the training data for this purpose.
The document Csató, Lehel; Opper, Manfred, “Sparse On-Line Gaussian Processes,” Neural Computation 14, pp. 641-668, 2002 discloses a method for identifying interpolation point data for a sparse Gaussian process model.
Other methods relevant in this regard are known from Smola, A. J., Schölkopf, W., “Sparse Greedy Gaussian Process Regression,” Advances in Neural Information Processing Systems 13, pp. 619-625, 2001; and Seeger, M., Williams, C. K., Lawrence, N. D., “Fast Forward Selection to Speed up Sparse Gaussian Process Regression,” Proceedings of the 9th International Workshop on Artificial Intelligence and Statistics, 2003.